Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, x > 5 means x is greater than 5.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, x < 3 means x is less than 3.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is greater than or equal to 4.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is less than or equal to 2.

Front

How do you solve the inequality 2x + 3 < 7?

Back

Subtract 3 from both sides: 2x < 4. Then divide by 2: x < 2.

Front

What is the solution to the inequality 84 - 4x ≤ 52?

Back

Subtract 84 from both sides: -4x ≤ -32. Then divide by -4 (remember to flip the inequality): x ≥ 8.

Front

How do you represent a situation where you need to practice at least 50 minutes?

Back

You can represent it with the inequality 28 + 2x ≥ 50, where x is the time practiced in the afternoon.

Front

What type of circle is used when graphing the inequality x < 3?

Back

An open circle is used for < and >, indicating that the endpoint is not included.

Front

What type of circle is used when graphing the inequality x ≤ 5?

Back

A closed circle is used for ≤ and ≥, indicating that the endpoint is included.